learning visualization strategies: a qualitative investigation
TRANSCRIPT
Full Terms & Conditions of access and use can be found athttp://www.tandfonline.com/action/journalInformation?journalCode=tsed20
Download by: [Orta Dogu Teknik Universitesi] Date: 06 February 2016, At: 01:55
International Journal of Science Education
ISSN: 0950-0693 (Print) 1464-5289 (Online) Journal homepage: http://www.tandfonline.com/loi/tsed20
Learning Visualization Strategies: A qualitativeinvestigation
Daniel Halpern, Kyong Eun Oh, Marilyn Tremaine, James Chiang, KarenBemis & Deborah Silver
To cite this article: Daniel Halpern, Kyong Eun Oh, Marilyn Tremaine, James Chiang,Karen Bemis & Deborah Silver (2015) Learning Visualization Strategies: A qualitativeinvestigation, International Journal of Science Education, 37:18, 3038-3065, DOI:10.1080/09500693.2015.1116128
To link to this article: http://dx.doi.org/10.1080/09500693.2015.1116128
Published online: 01 Feb 2016.
Submit your article to this journal
Article views: 36
View related articles
View Crossmark data
Learning Visualization Strategies:A qualitative investigation
Daniel Halperna∗, Kyong Eun Ohb, Marilyn Tremainec,James Chiangc, Karen Bemisd and Deborah SilvercaSchool of Communications, Pontificia Universidad Catolica de Chile, Santiago, Chile;bGraduate School of Library and Information Science, Simmons College, Boston, MA,USA; cElectrical and Computer Engineering, Rutgers, the State University of New Jersey,Piscataway, NJ, USA; dInstitute of Marine and Costal Sciences, School of Environmentaland Biological Sciences, Rutgers, the State University of New Jersey, New Brunswick, NJ,USA
The following study investigates the range of strategies individuals develop to infer and interpretcross-sections of three-dimensional objects. We focus on the identification of mentalrepresentations and problem-solving processes made by 11 individuals with the goal of buildingtraining applications that integrate the strategies developed by the participants in our study. Ourresults suggest that although spatial transformation and perspective-taking techniques are usefulfor visualizing cross-section problems, these visual processes are augmented by analytical thinking.Further, our study shows that participants employ general analytic strategies for extended periodswhich evolve through practice into a set of progressively more expert strategies. Theoreticalimplications are discussed and five main findings are recommended for integration into the designof education software that facilitates visual learning and comprehension.
Keywords: Visual learning; 3D visualization; Spatial transformation; Spatial problem-solving; Perspective-taking; Visual comprehension
Visualizations have traditionally been used in science as an additional resource for tea-chers to help students to understand abstract concepts that are difficult to describe orphenomena that cannot be observed directly (Buckley, 2000). Science ‘visualizations’present data in novel ways to foster student comprehension (Gilbert, 2007). As Mayerand Gallini (1990) suggest, despite the bias toward verbal over visual forms of
International Journal of Science Education, 2015Vol. 37, No. 18, 3038–3065, http://dx.doi.org/10.1080/09500693.2015.1116128
∗Corresponding author. School of Communications, Pontificia Universidad Catolica de Chile,Alameda 340, Santiago, Chile. Emails: [email protected], [email protected]
© 2016 Taylor & Francis
Dow
nloa
ded
by [
Ort
a D
ogu
Tek
nik
Uni
vers
itesi
] at
01:
55 0
6 Fe
brua
ry 2
016
instruction, research has found a tremendous potential in visually based instruction tofacilitate students’ understanding of scientific material. In fact, even ‘non-spatial’ pro-blems are more effectively addressed by the insertion of visualizations (Wu & Shah,2004), and there is a consensus among scholars that student achievement in scienceis generally supported by direct access to multimedia modes of representation (Uttal& Doherty, 2008). In chemistry for instance, by visualizing sketched structures,symbols, arrows and equations, students can actually ‘see’ the chemical process(Kozma, Chin, Russell, &Marx, 2000). These chemical representations allow learnersto think visually and convey information efficiently through a form of visual display(Wu & Shah, 2004).Rapp and Kurby (2008) explain that by making visually explicit complex processes,
these visualizations facilitate students’ ability to make new links between concepts theyalready know with the science being explained: if students know, for instance, that par-ticular colors are associated with specific temperatures (e.g. red represents hot), theycan use the information to quickly understand the meaning of color cues in a depth-related water, earth or air temperature diagram. However, research has consistentlyfound that students exhibit difficulties in interpreting cross-section visualizationsand anatomical structures (Russell-Gebbett, 1985), one of the most utilized represen-tations in science. Treagust, Chittleborough, and Mamiala (2003) report that learnersexperience difficulties in connecting properties of a molecule with its formula, whereasin chemistry and geology students have difficulties in interpreting symbolic represen-tations and transforming them into three-dimensional (3D) structures (Furió &Calatayud, 1996).Similarly, Kali and Orion (1996) studied the 3D spatial abilities of geology stu-
dents by measuring their capacity to comprehend the 3D structure of folded sedi-mentary rocks from surface structure visualizations. They found that students haddifferent Visual Penetrative Ability, which is ‘the ability mentally to penetrate theimage of a structure’ (Kali & Orion, 1996, p. 369) when solving geology problems.Some of them could not associate the surface information of the geological struc-tures with their interior. These studies indicate that students, paradoxically, haveproblems in comprehending the very images designed to facilitate their under-standing, and thus, illustrate the importance to consider not only how visualiza-tions are designed, but also the way they are interpreted (Pozzer-Ardenghi &Roth, 2005).Not surprisingly, research shows that spatial intelligence plays a central role in
learning through use of visualizations. These are the capabilities to perceive thevisual world accurately, to develop transformations upon individual’s visualexperience, even in the absence of physical stimulation (Gilbert, 2007).Further, several studies have demonstrated that spatial intelligence can be devel-oped through training, instruction in academic settings (Wright, Thompson,Ganis, Newcombe, & Kosslyn, 2008), and even by playing video games (Feng,Spence, & Pratt, 2007). Piburn et al. (2005) designed an experiment to assessthe role of spatial ability in learning geology using multimedia instructionalmodules that used visualizations. They found that subjects improved their
Learning 3D Visualization Strategies 3039
Dow
nloa
ded
by [
Ort
a D
ogu
Tek
nik
Uni
vers
itesi
] at
01:
55 0
6 Fe
brua
ry 2
016
spatial visualization and geospatial examination, demonstrating that spatial abilityis improved through instruction. Nevertheless, little research has been done onhow individuals learn from similar sets of problems and then develop their ownstrategies to solve visualization tasks.For this purpose, a test using 3D block visualization problems was designed to
gain a deeper understanding about the learning process and strategies developedby individuals in order to visualize the internal structure of 3D visualizations.This technique, which attempts to provide the visual experience of the real worldto users, has become a relevant tool for learning purposes in geology, where stu-dents have to understand the different layers underneath geological structures(Kali & Orion, 1996). More specifically, cross-sections of 3D objects have been fre-quently used in textbooks to help students gain a better understanding of the under-lying object. Loosely defined by Russel-Gebbett (1985) as the flat surface thatcomes out when a 3D object is cut by a 2D plane, these types of representationsthat require observers to mentally visualize the underlying features of the structuredepicted have become the standard practice in many disciplines of science.Research in this area has focused on how accurately students visualize the internalproperties of the 3D diagrams by centering on problem-solving tasks (Kali & Orion,1996). Figure 1 shows different cross-section problems in which subjects wereasked to imagine how the layer that the slice cuts looks and then to draw the result-ing cross-sectional slice.Because particular attention was paid to the reasoning processes of participants
as they tried to overcome the difficulties of the diagrams that prevented their
Figure 1 (a) Presents a stimulus of 3D object showing the cutting plane and viewing-directionarrow for one trial, and below the arrow view for the trial shown (Keehner et al., 2008); (b)Shows one of the tasks by Kali and Orion (1996) to determine the level of visual penetrationability in students, and (c) presents an integrative quiz question asking students to place the
events (faulting versus intrusion) in the order they must have happened (Piburn et al., 2005)
3040 D. Halpern et al.
Dow
nloa
ded
by [
Ort
a D
ogu
Tek
nik
Uni
vers
itesi
] at
01:
55 0
6 Fe
brua
ry 2
016
comprehension, we believe the conclusions obtained in the analysis may be useful tointegrate into the design of intelligent software that facilitates internal visual learningand comprehension processes.
1. Literature Review
Research has suggested that spatial intelligence is central to careers that required highspatial reasoning levels such as geology (Kali & Orion, 1996). Consequently, discover-ing how to increase one’s level of spatial abilities is relevant for basic education.However, spatial abilities are not typically taught as part of core education practicesand thus, are rarely considered as influential on students’ academic performance(Webb, Lubinski, & Benbow, 2007). Auspiciously, numerous studies suggest that per-formance on spatial tasks can be improved through training (Tzuriel & Egozi, 2010)and that practice in different domains may serve to improve other spatial abilities(Terlecki, Newcombe, & Little, 2008).
1.1. Learning Visualizations Strategies: An holistic approach
Since 1920, factor analytic studies have explored how subjects employ different strat-egies to solve spatial tasks, distinguishing between mental rotation and perspective-taking processes (Wraga, Creem, Profitt, & Proffitt, 2000). The former includesthose abilities related to manipulating images of spatial patterns internally and com-prehending imaginary movements in 3D spaces (mental rotation processes),whereas the later to measuring abilities associated with spatial relations in which thebody orientation of the observer is an essential part of the problem, for example, ima-gining how a stimulus array will appear from another perspective (perspective-takingprocesses). However, researchers have also noted a third strategy set in which individ-uals rely on the use of analytic processes to solve tasks based on non-spatial infor-mation (Linn & Petersen, 1985). In fact, studies in the early 1960s have alreadymentioned the possibility that respondents could use analytic processes to rotatefigures when mental rotation becomes a more complex task than an analytic approach(French, Ekstrom, & Price, 1969).
Indeed, the distinction between spatial or ‘holistic’ strategies, which involve analyticreasoning rather than mental manipulation of objects, is very common in the spatialability literature (Hegarty, 2010). Black (2005) reports a variety of domain-specificanalytic strategies used by subjects in a laboratory-based task to solve spatial abilityproblems with little to no use of spatial information, concluding that once participantsdevelop an analytical rule as they try to solve a problem, subjects switch to this rule-based strategy and no longer report the use of imagistic strategies to visualize a sol-ution. Similarly, Stieff and Raje (2008) found that the majority of problem-solvingapproaches in experts solving chemistry problems were characterized by analytic strat-egies, whereas Linn and Petersen (1985) reported that in solving cross-section pro-blems, those individuals who were able to develop a repertoire of strategies werealso those who performed well on the problems.
Learning 3D Visualization Strategies 3041
Dow
nloa
ded
by [
Ort
a D
ogu
Tek
nik
Uni
vers
itesi
] at
01:
55 0
6 Fe
brua
ry 2
016
Further, research by Keehner, Hegarty, Cohen, Khooshabeh, and Montello (2008)found that most subjects decompose tasks to solve cross-section problems: first theydetermine the outside shape of the cross-section, then they try to see how manyducts there should be in the drawn cross-section, afterward they determine theshape of the ducts and finally they infer where the ducts should be. Moreover,Hegarty (2010) argues that the best spatial thinkers are those who augment visualiza-tion with analytic strategies in order to visualize only the information that they need totransform and solve a problem. Overall, these studies suggest that bothmental rotationand perceptive-taking processes are augmented by more analytic forms of thinkingsuch as task decomposition and rule-based reasoning.
1.2. Visualization Through a Problem-Solving Lens
Problem-solving skills are commonly considered one of the most relevant professionalcognitive activities and highly valued in contemporary learning theories (Sweller,1988). The implementation and discovery of strategies for problem solving has beencomprehensively examined in the education literature. Siegler (2006) explains thatadoption of new strategies is slow since prior strategies persist even when the newlydiscovered strategy has clear advantages. Research has shown that individuals donot switch abruptly from using ineffective strategies to effective expert-like strategies,but rather employ more general strategies first (e.g. trial and error, means-ends analy-sis) for extended periods and then, as they slowly practice and increase their knowl-edge in the area, develop more heuristics and expert analytic strategies (Stieff &Raje, 2008).
Problem-solving can be loosely defined as a goal-oriented sequence of cognitiveoperations. The extant literature has distinguished two main groups of strategies inproblem-solving: search-based mechanisms and schema-driven processes (Gick,1986). Search-based mechanisms are used by novices, and the most general strategywithin this group is the means-ends analysis, which is related to the reduction of thedifference between the current state and the goal of the problem. Newell and Simon(1972) explain that problem solvers first understand the goal of the problem andthen look for problem-solving operators. If the solution is successful, the task isover. If it fails, the solver backtracks to an earlier stage and attempts to redefine theproblem or use another method to solve it.Through schema-driven processes, on the other hand, experts are able to work
forward immediately by choosing appropriate steps that lead them to their goal asthey recognize the problem from previous experiences and already know the nextmoves to solve it. This schema-driven process is activated heuristically as a data-driven response to some related cue in the problem (Chi, Feltovich, & Glaser,1981). Once the schema is activated, the knowledge contained in the schema pro-vides the general steps and procedures to follow in order to solve the problem.The knowledge of experts thereby, should be considered as ‘coherent chunks ofinformation organized around underlying principles in the domain’ (Cook, 2006,p. 1078), which is used to perceive underlying patterns and principles in problem
3042 D. Halpern et al.
Dow
nloa
ded
by [
Ort
a D
ogu
Tek
nik
Uni
vers
itesi
] at
01:
55 0
6 Fe
brua
ry 2
016
situations. In contrast, novices virtually ‘see’ a problem differently since they donot possess appropriate schemas, and consequently cannot recognize problem con-figurations. Thus, they have to use more general problem-solving strategies suchas means-ends analysis or processes that are based on hierarchical task decompo-sition (Gick, 1986).
1.3. Visualization in Science Education: How can this be used for learning?
Research on learning with visualizations has demonstrated that once learners interactwith appropriate representations their academic performance is enhanced (Ainsworth,2006). Two main theories in the problem-solving literature that bases instructionaldesign principles on learners’ cognitive structures have been used to explain the learn-ing attained by students through visualizations (Cook, 2006): (1) the distributed cog-nition framework and (2) theoretical models that view visual and analytic reasoning ascomplements. The basic premise of the distributed cognition framework is that learn-ing processes are hindered when the instructional materials overcome the cognitiveresources. This framework holds that there is a cognitive architecture consisting of alimited working memory that interacts with an unlimited long-term memory(Sweller, 2004). Thus, the overload on working memory could be decreased byeither augmenting its capacity or reducing its cognitive load. In fact, the external rep-resentations that subjects use for problem-solving is not just a marginal assistance tocognition, but rather, they are strongly related to the internal cognitive processes.By using visualization techniques, a distributed representational space is created inthe subjects’ minds, which could help them in turn, to solve a problem using theseadditional resources.Regarding theoretical models that view visual and analytic reasoning as comp-
lements, the literature in problem-solving indicates that in order to construct aricher understanding of the processes that take place during problem-solving thatinvolves visual representation use, learners need to integrate both visual and analyticthinking (Presmeg, 1992; Stylianou, 2002; Zazkis, Dubinsky, & Dautermann,1996). The Visualizer/Analyzer (V/A) model, for example, holds that visualizationand analysis, although distinct forms of thinking, inform one another and worktogether in the process of problem-solving (Stylianou, 2002). It is expressed interms of discrete levels of visual and analytic thinking, as an approximation of the con-tinuous thinking of the learners. The analysis described by the model begins with anact of visualization, V1. The next step is an act of analysis, A1, which consists ofsome kind of reasoning about the objects constructed in step V1. This is followedby a subsequent act of visualization, V2, in which the subject returns to the same‘picture’ used in V1, but reasoning is enriched as a result of A1. That leads to asecond act of analysis, A2, which is followed by a third step of visualization, V3, andso on. The iteration ends as the problem solver comes to a better understanding ofthe problem he/she is solving.An extension of prior studies on problem-solving in the visualization area which ana-
lyzes how individuals learn from similar sets of problems and begin to develop their
Learning 3D Visualization Strategies 3043
Dow
nloa
ded
by [
Ort
a D
ogu
Tek
nik
Uni
vers
itesi
] at
01:
55 0
6 Fe
brua
ry 2
016
own problem-solving strategies is an appropriate next step to take. Our work begins totake this next step. As research has shown, cross-section problems provide an excellentopportunity to study the role of alternative strategy choice in problem-solving (Kali &Orion, 1996; Stieff & Raje, 2008).
1.4. This Study
We present a qualitative study designed to understand the learning process and strat-egies employed by individuals to visualize internal structures of 3D visualizations. Thestudy aims to analyze the strategies developed by participants to overcome the com-plexity of diagram properties that prevent their comprehension. Based on previousfindings that both mental rotation and perceptive-taking processes are augmentedby more analytic forms of thinking and that, with practice, individuals develop andimplement more heuristics and expert analytic strategies, we aim to answer tworesearch questions:
RQ1:What types of strategies do individuals develop to infer cross-sections of 3D objects?RQ2: Could individuals learn from using similar sets of problems to more effectivelydevelop analytic strategies to solve visualization tasks?
The answers to these research questions are very relevant to us since the third goalof this paper and our overall research is to develop intelligent software able toenhance the learning process and the acquisition of viable analytic problem-solvingstrategies. Several studies have shown that visualization software can enhance 3Dgeometric proficiency by improving a user’s abilities to build spatial images (Haupt-man, 2010). Shneiderman (1997) has suggested the potential benefits of using phys-ically based or tangible interfaces to enhance spatial skills and improve a user’sabilities to build spatial images. Our research is based on the idea that cognitivebenefits result from manipulating physical materials, and that mental processingbenefits from using concrete physical objects designed to support more natural learn-ing. Marshall (2007) explains that because tangible interfaces often utilize concretephysical manipulation, they might support more effective or more natural learning,consequently 3D forms would be perceived more readily through tangible represen-tations than through visual representation alone. Further, consistent with the Cogni-tive Theory of Multimedia Learning (Mayer & Moreno, 1998), the advantages thatexternal representations play in supporting learning are: (1) they reduce the amountof cognitive effort required to solve equivalent problems (Larkin, McDermott,Simon, & Simon, 1980); (2) they help to assimilate cognitively the content pre-sented, as users interact with the figures virtually (which serves as a copy of thereal world) (Mayer & Moreno, 1998); and (3) they hasten the learning process, asthe virtual figures generated by the software gives the user intuitive freedom ofaction to interact in an unlimited manner with the objects in the virtual environment(Winn & Jackson, 1999). Thus, answers to both research questions will suggestdesign solutions for a software package intended to foster the strategies developedby the participants in our study
3044 D. Halpern et al.
Dow
nloa
ded
by [
Ort
a D
ogu
Tek
nik
Uni
vers
itesi
] at
01:
55 0
6 Fe
brua
ry 2
016
2. Methodology
Eleven undergraduate students were videotaped as they attempted to solve 18 ‘slice’visualization problems. They were asked to visualize the internal structure of 3D visu-alization diagrams by drawing what the cut face of the visualization would look like if itwere cut internally along the dotted lines shown on the figure. Each slice visualizationproblem was drawn on the top part of an individual sheet of paper. The problems wereordered in increasing difficulty as determined by a panel of experts in this type of visu-alization. Table 1 shows all the slice visualization problems we used where the firstexercise is the easiest one and the 18th is the most difficult one.Subjects were asked to draw the cut plane of the 3D visualizations on the bottom part
of the sheet of paper, while thinking aloud and expressing the difficulties they faced. Thisprocess, which is known in the literature as a think aloud protocol, has been used toexamine the cognitive processes in different disciplines, and it was chosen becausesuch verbalizations present an opportunity to make students’ reasoning more coherentand reflective (Ericsson & Simon, 1998). In our study, the interviewer gently remindedparticipants to ‘keep talking’ while solving the problems. When subjects finisheddrawing the slice, the interviewer asked participants to review the steps followed inorder to get more information about the processes behind their actions. Then the sol-ution to the task was given and participants were allowed to compare it with theiranswers. Subjects were asked to stop after an hour even if they did not finish the 18 pro-blems. Ten subjects did not complete the entire set of problems.
2.1. Participants
Participants were students from Communication departments and Engineeringdepartments at our university. We focused on recruiting half of our participantsfrom non-science disciplines since such individuals are likely to have lower spatial abil-ities. Among the 11 participants, 6 were male and 5 were female. Their ages rangedfrom 18 to 26.
2.2. Generation of 3D Visualization Diagrams
The visualizations used in this study were black and white 2D representations of 3Ddiagrams with different patterns used to represent internal layers. The 3D visualiza-tions had virtual slices drawn through them that were represented by the letters A,B and C connected by a dotted line, as is shown in Figure 2. The patterns can beobserved in the figures presented in Table 1. The diagrams contained multiple prop-erties that represented features of visualizations that typical cross-sections contain(Kali & Orion, 1996). To generate the diagrams, a set of representative 3D visualiza-tions were collected from introductory Geology and Earth Science textbooks. Theslice visualization problems were ordered from easiest to hardest for presentation toparticipants by asking seven experts and two novices to solve 32 visualization problemsand rank-order these problems by difficulty. Group consensus was then used to select18 ordered problems in which all difficulty judging participants agreed on their order.
Learning 3D Visualization Strategies 3045
Dow
nloa
ded
by [
Ort
a D
ogu
Tek
nik
Uni
vers
itesi
] at
01:
55 0
6 Fe
brua
ry 2
016
Table 1. Descriptive data for slice visualization problems
ID Diagram CorrectsPerspective
takingSpatial
transformationAnalyticstrategies
Developingstrategies
1 11 7 0 1 0
2 11 8 2 1 0
3 10 12 2 2 0
4 11 8 3 3 0
5 10 15 4 5 0
6 8 25 5 12 0
7 6 16 5 7 0
8 7 23 7 14 0
9 6 22 6 21 2
(Continued)
3046 D. Halpern et al.
Dow
nloa
ded
by [
Ort
a D
ogu
Tek
nik
Uni
vers
itesi
] at
01:
55 0
6 Fe
brua
ry 2
016
Table 1. Continued
ID Diagram CorrectsPerspective
takingSpatial
transformationAnalyticstrategies
Developingstrategies
10 5 21 6 23 2
11 4 20 6 22 2
12 4 15 5 19 2
13 3 11 4 14 2
14 2 11 4 13 1
15 2 10 4 12 1
16 1 8 2 10 1
17 1 7 2 9 1
(Continued)
Learning 3D Visualization Strategies 3047
Dow
nloa
ded
by [
Ort
a D
ogu
Tek
nik
Uni
vers
itesi
] at
01:
55 0
6 Fe
brua
ry 2
016
2.3. Operationalization of Key Terminologies
. 3D visualization problems: 18 3D visualization diagrams were given to participants.
. Planes of presentation: A viewer’s automatically assumed x, y and z coordinatesystem (Heo & Hirtle, 2001).
. Cut: The plane that slices 3D visualizations into two pieces. It is often referred to asa cross-section in different fields (Cohen & Hegarty, 2007; Kali & Orion, 1996).
. Action: Any movement, gesture, sketching or verbalization generated by the partici-pant while solving the 3D visualization problems.
2.4. Data Analysis
In order to identify inductively the problem-solving strategies developed by partici-pants, verbal protocols as well as subjects’ gestures and drawings were analyzed. Forthis purpose, we used Transana (http://www.transana.org/), a qualitative analysis
Table 1. Continued
ID Diagram CorrectsPerspective
takingSpatial
transformationAnalyticstrategies
Developingstrategies
18 1 7 2 9 1
Note: The table shows how many participants drew accurately each one of the 18 diagrams and thenumber of strategies employed for this purpose.
Figure 2. The x and y axes form one plane. The x and z axes another with the y and z axes the thirdplane. Because the figure is presented as a block, the viewer automatically assumes that the shown x,y and z axes are the coordinate system in use. The dotted line through the block shows the cross-
section or cutting plane
3048 D. Halpern et al.
Dow
nloa
ded
by [
Ort
a D
ogu
Tek
nik
Uni
vers
itesi
] at
01:
55 0
6 Fe
brua
ry 2
016
software for video and audio data. The transcription of each interview was analyzedusing established techniques in previous verbal protocol studies (Ericsson & Simon,1998). Each problem-solving exercise was regarded as an independent unit, andeach participant’s utterances and behaviors trying to solve the problem were analyzedto identify the actions used. We analyzed the data in four steps. First, we transcribedeach of the video recordings, and as we analyzed the transcription, we identified pat-terns employed by subjects to solve the tasks in order to have a narrative depiction ofthe actions. Thus, this first phase of data analysis was designed to identify actions thatultimately would be leading participants to develop a strategy. We began the analysisusing the process of theoretical coding (Glaser, 1978) by examining the videos and thetranscripts actions that appeared to lead participants to problem solutions, and appliedcodes to these instances. In total, 24 distinct codes were produced.The next step of analysis was axial coding. This involved reassembling the coded
data in new ways by grouping codes that were conceptually similar (Charmaz,2006). The third data analysis phase was designed to confirm the codes utilized to cat-egorize the actions. For this purpose, each video recording was viewed more than fivetimes by three researchers until all agree on the actions employed by participants tosolve the problems. As we observed the video recordings multiple times, a table wasdeveloped based on the agreement of the researchers. A portion of this table is pre-sented in Table 2, where it can be seen as a description of the actions developed byparticipants, the physical gestures used to fulfill the actions and some excerpts ofthe transcription that illustrate how the subjects verbalized their efforts to solve theproblems by using these actions.Finally, to corroborate the coding, we followed the approach taken by Stieff and
Raje (2008) in order to identify strategies. First, the frequency and order of theactions were analyzed to understand which specific actions led subjects to develop par-ticular strategies. We compared the tables of actions employed by each participant inorder to identify sequences of actions before participants began to implement a strat-egy. In this way, we also could see whether subjects learned from earlier problems andused this learning to develop strategies that they then applied to their next visualizationtask. Once we finished the comparison of the actions employed by participants, wecould determine whether students were employing similar strategies as will beshown below. It is relevant for us to note that after participant number eight, we didnot find any action or new strategy employed by the three last individuals. Thus,after 11 videotapings, we decided to not videotape more participants. We may havemissed more potential strategies, but felt that the accumulations of knowledge thatwe had already obtained was sufficient to begin experiments to further verify ourresults and also being the development of a sequence of visualization slice problemsthat would aid in the learning of these analytic strategies.
3. Results
Only one of the subjects completed the 18 exercises accurately in 1 hour. Two partici-pants completed 14 problems, two subjects solved 10, two participants solved eight
Learning 3D Visualization Strategies 3049
Dow
nloa
ded
by [
Ort
a D
ogu
Tek
nik
Uni
vers
itesi
] at
01:
55 0
6 Fe
brua
ry 2
016
and three participants solved up until problem number 6. Problem number 4 was thelast one that all the participants solved it accurately. Table 1 shows the different pro-blems, how many participants accurately drew accurately each one of them and thenumber of strategies employed by each participant for this purpose.Answers were considered correct if the general pattern of the layers was accurate.
Inaccuracies in depicting the thickness of layers, or their precise location in thecross-section, were also ignored. Figures 3 and 4 show accurate and inaccurate depic-tions of the cut face draw by participants. Our analysis found subjects employing avariety of actions and strategies to visualize the internal structure of the 3D diagramswith diverse degrees of effectiveness. The results indicated actions related to perspec-tive-taking, spatial transformation and analytical processes.
Table 2. Example of a table developed while analyzing data in one of the subjects until problemeight
#F Actions identified in participantGestures made by the
participantExcerpt of the transcription in each
action
1 Compares the cut/slice with thefront face of shape
Indicates the front If I look at here, I should knowwhere the cut starts
1 Compares angles to estimate theportion of the pattern
Moves from the cut tothe front face
There is perspective here, it shouldbe tall here
2 Compares the cut/slice with thefront face of shape
Uses fingers tomeasure
Through this way I know theproportions are ok
3 Rotates head to visualize theslice and patterns of diagram
Physically rotates/moves the paper
So we need to rotate it
3 Rotates figure to solve problem(put the cut vertical)
Rotates paper Like the other images I will have torotate…
4 Comparing the cut/slice with theprevious ones
Indicating the cut/slice
This looks like a cube and it shouldbe a rectangle
4 Draws lines checking figure withproportion in diagram
Marks the diagram tomeasure
Through this way I can calculatebetter the size
4 Identifies the easier point of viewto visualize the image
Looks the diagramand moves it
Before the way the angle was cutwas from behind…
5 Rotates in his mind the cut fromhorizontal to vertical
Rotates paper I could rotate it but now I feel okvisualizing it from the top
5 Contrasts the position of thelines with the rest of the figure
Draws lines parallel tothe figure
This layer has the lines, I’m gettinga little confuse… .
5 Draws lines to visualize therotation of the figure
Draws outside thefigure
Through this I can understand thecut
6 Compares the faces of the figurein order to gain information
Looks the overallshape of the diagram
It looks pretty much like a cub andI can gain information…
6 Identifies what the cut wouldinclude based on the front face
Shows the parts he isnot including
I’m not concerned about thisbecause I assume it’s under the cut
6 The use of external elements/experiences to visualize the cut
Draws a figure outsidethe diagram
I’m imagining a cake
Note: The first column shows the action employed by the subject, the second one the gestures andthe third column shows excerpt of the transcription in each action.
3050 D. Halpern et al.
Dow
nloa
ded
by [
Ort
a D
ogu
Tek
nik
Uni
vers
itesi
] at
01:
55 0
6 Fe
brua
ry 2
016
Regarding the analysis, axial coding resulted in a reclassification into eight maincodes indicating actions related to three categories. The most common one, perspec-tive-taking strategies, included three actions: head rotation (the rotation of the partici-pant’s head in one direction or another), sheet rotation (the rotation of the sheet ofpaper containing the problem) and letter labeling (participants labeled the letters inthe problem’s solutions in order to orient the solution regarding the problems. Thesecond category, spatial transformation strategies, only included the mental rotationof the problem (this was learned through the verbal protocol). The third, analytic
Figure 4. These examples show accurate drawings of the problems, although the thickness of layersor their precise location in the cross-section were not 100% correct: (a) shows the first layer wider towhat it should be, in (b) the last layer should be thinner, and in (c) the form of the layer with cubes
should be more in diagonal
Figure 3. It shows the most frequent errors made by subjects. (a) Illustrates how the subject did notconsider one of the layers. A similar error can be observed in (b). The drawing in (c) shows an errorwith the perspective adopted by the subject, who could not visualize the angle of the cut face and only
copied one of the faces
Learning 3D Visualization Strategies 3051
Dow
nloa
ded
by [
Ort
a D
ogu
Tek
nik
Uni
vers
itesi
] at
01:
55 0
6 Fe
brua
ry 2
016
strategies, considered four actions: blocking information to see a portion of the figurewithout interference from other parts, drawing what would be external extensions ofthe patterns shown on the outside of a figure, measuring and contrasting the lines ofthe figure with the drawing to make it proportional (by comparing the relative sizesand relationships of visible features and using these to determine the sizes and relation-ships of features in the slice) and actions related to the decomposition of the problem,such as dividing the exercise into parts as will be shown below.
3.1. Perspective-Taking Strategies
We define a perspective-taking strategy as one in which the participant attempts tochange his or her point of view of the 3D object in an attempt to make the problemeasier to visualize. Perspective-taking-oriented actions were the most simple and fre-quent strategies found in the study, as can be observed in Table 1. We identifiedthree categories of actions related to this strategy. The most common action was chan-ging the position of the head in relation to the problem. All the participants, at somemoment during the study, rotated their heads in order to virtually arrange their pos-ition to be one parallel to the front face of the diagram. For example, they eithertipped their heads sideways to the left or right in order to be looking at the 3Dfigure from the left front side or right front side, respectively. The second actionwas the rotation of the problem sheets orienting them to different positions in orderto look for a better angle that allowed them to see parts of the problem in a new x–zplane. This was observed in 10 of the participants.Participants were aware of choosing a different perspective to visualize the problem.
Subject 3, for example, once she finished problem 9 and was asked about the actionsshe used it in order to solve the problem, stated that she used a top-down approach tovisualize it. ‘I felt much more comfortable seeing the slice from here [showing the topface] than from the bottom, since it is easier for me to take this part off [showing thepart below the dotted lines]’. Similarly, eight of the participants mentioned, at least inone of the exercises, that they had changed their perspective regarding the represen-tation of the object. Interestingly, seven of the eight participants who used a self-refer-ential position to visualize the problems employed this action when they solvedproblem number 6, the first task in which the cutting plane was both horizontal andat an angle (this is shown in Table 1). In the prior problems, participants couldimagine themselves viewing the problem solution by either positioning in front ofthe x–z plane of the figure or in front of the x–y plane. With problem 6, they neededto imagine themselves looking down on the figure or up at it. Problem 6 records thehighest number of actions (25) related to this strategy, as shown in Table 1, demon-strating that participants had to employ these types of actions in order to accuratelysolve the problem. Eight of the 11 participants solved this problem. It was in this exer-cise that subjects started to mention that they were taking a bottom-up or top-downview, instead of using a frontal perspective. Participants who showed a higher flexibilityin shifting their referential points and looked at the figures from different perspectivesperformed better than those who did not indicate this skill: Seven of the individuals
3052 D. Halpern et al.
Dow
nloa
ded
by [
Ort
a D
ogu
Tek
nik
Uni
vers
itesi
] at
01:
55 0
6 Fe
brua
ry 2
016
who applied this strategy in problem 6 accurately solved problem 8 (which required asimilar approach).The third perspective-taking action identified was used to determine the relative
position of the spatially arranged items in the diagram. Ten of the subjects labeledeach corner of their slice with the letters ABCD, imitating the original cut shown inthe problem. This lettering served as reference points and was used to orient the sub-jects. Participants gave a similar reason to explain their actions: ‘Putting the lettershelps me to know where I am when I compare my drawing with the figure and howI need to continue’ (Subject 3); ‘It is easier to know in which part of the exercise Iam and the perspective from where I’m solving the problem’ (Subject 5).
3.2. Spatial Transformation Strategies
Spatial transformation strategies are those which focus on manipulating images ofspatial patterns internally and comprehending imaginary movements in 3D spaces.The only action identified was a 90 degrees rotation of the problem using the letterson the cut plane of the diagram as a point of reference. In fact, as Table 1 shows,this was the strategy least used by participants. The other spatial transformationactions were mixed with analytical processes as will be explained in the next section.In problem 6, for example, as was mentioned before, two subjects indicated explicitlyat the end of the exercise that they rotated the block mentally. Subject 6, for example,explained: ‘I think it’s much more difficult for me to see horizontal cuts because wedon’t cut cakes horizontally, we do this vertically, and I think I am more used tothat’. The action used by participants to transform the figure spatially was to draw asquare/rectangle representing the cut plane and copy the letters of the cross-sectionas points of reference on to this plane. Then, based on these points of reference,rotate the shape of their drawings (from horizontal to vertical) in their mind. This strat-egy was recognized in eight participants. Subject 1, for example, said: ‘I have a realneed for rotation, I need the rotation if I have B here… So I’m going to stick to thesame A, B, D, C case here, that will be easier for me’.However, it is important to note that after problem 9, none of the participants were
able to mentally manipulate the cutting plane without external visual aids (e.g. bydrawing an additional figure representing a portion of the original figure) or byusing a learned analytical process (task decomposition). In fact, those who tried tosolely visualize the problems in their minds could not solve them without thisadditional external help. Participant 1 tried first to rotate the figure mentally, butsoon realized he could not visualize the problem internally: ‘This cross section has alayer that should come into view on the other side [trying to picture the other side]… but I don’t know… I guess it is difficult’. Subjects who relied only on internal pro-cesses were so concentrated on visualizing the cross-sections that they could not evencorrectly verbalize their thoughts. For example, participant 5 said, ‘It is cutting it thisway [pointing at the cut with the pen], sort of [pausing]. Hmm… not actually sure[pausing]…Uh… [pointing at the cut with the pen again] I can’t really tell it’scutting at a diagonal’.
Learning 3D Visualization Strategies 3053
Dow
nloa
ded
by [
Ort
a D
ogu
Tek
nik
Uni
vers
itesi
] at
01:
55 0
6 Fe
brua
ry 2
016
3.3. Analytic Strategies
Analytic strategies involve reasoning rather than mental manipulation of objects inwhich the problem solver uses a general rule to create a solution. It is important tonote that most of these actions were employed as the difficulty of the problemsincreases. In fact, Table 1 shows that during the first problems none of the participantsapplied them. We identified three main categories of analytic strategies. For the firstcategory, we grouped two actions intended to reduce the memory load when visualiz-ing internal patterns (layers) crossed by the cutting plane: (1) The blocking of irrele-vant information by participants—most of the subjects used their hands to physicallyenclose the cutting plane and hide the rest of the problem, as Figure 5(b) and 5(c)show—and (2) The creation of extended lines to mark out the area enclosed by thecross-section, as is shown in Figure 5(a). These two actions were employed by 10 ofthe subjects, and some of the participants even developed a sequence of actions toenclose the cross-section, as Participant 3 noted:
I wanted to do the same thing, to draw this face, and mentally block the rest [covering thediagram with her hands], but then I tried to do a new thing, to draw the invisible line inorder to make it easier to get the slice [she draws lines over the cross section uncoveringthe lines of the plane].
When participants were asked why they employed these actions, they indicated thatthey felt confused by the additional sections of the block diagram and wanted to avoidtoo much information by focusing only on the cross-section.The second category includes those actions directed at measuring the initial and
final layers that were included in the cross-section. This was done to assess possiblechanges in the patterns of the layers. Seven of the subjects marked reference pointsin the slices they were creating before drawing them in their answer in order to esti-mate, based on the marks, how the route or trajectory of the layers would change.
Figure 5. The arrows in (a) show the ‘invisible lines’ extended by the subject in order to visualizethe cross-section, whereas (b) and (c) show a subject blocking the information not used in the
diagram to enhance her vision on the problem and infer the cross-section
3054 D. Halpern et al.
Dow
nloa
ded
by [
Ort
a D
ogu
Tek
nik
Uni
vers
itesi
] at
01:
55 0
6 Fe
brua
ry 2
016
Their procedures were very similar: first they compared their drawing slice with theblock diagram, marking in each side of their slices where the layers should start, ascan be seen in Figure 6(a). Five of the individuals who applied this strategy startedfrom the corners of their drawing slices and then continued toward the center oftheir figures. Then they checked the different faces of the blocks in order to confirmthe proportions, as Figure 6(b) shows, identifying what they believed would be theend of the layers. Finally, they connected the points marked previously, showing thefinal routes followed by the layers, as is illustrated by Figure 6(c).
The third category identified consisted of a series of actions in which participantsdecomposed the problem into smaller units in order to visualize the cross-sectionthrough progressive steps. After problem 11, all the participants who accuratelydrew the cross-sections used this approach, especially in the most complicated pro-blems which contained embedded figures, as is shown in Table 1. This strategy waschosen in response to previous failures, since all the participants who employed thedecomposition technique first tried to visualize the layers encompassed by the cross-section directly and simultaneously, but then, when they realized that they were notsucceeding with this approach, they decided to modify it. As subject 7 noted: ‘Icouldn’t do everything at once, I couldn’t see everything so I had to breake it intosmall pieces in order to go step by step, approaching each part differently’. Participantstypically tried to first determine the basic figures or less complicated areas of thediagram that were part of the cross-section; then they looked at how the layersmight change based on the angle of the cutting plane; next they would determinethe cross-section shape of the more complicated figures; and finally they inferredwhat the overall cross-section might look like. This set of analytic actions matcheswhat Hegarty (1992) calls task decomposition. Table 1 shows that participants whodid not use these actions could not solve the advanced problems.
3.4. Developing Problem-Solving Strategies
This section presents the analytic strategy developed by two participants that was usedto understand the configurations of the layers. Both subjects arrived at this technique
Figure 6. The arrows in (a) note the first ‘reference marks’ that represent where the layers shouldstart. (b) Shows the subject assessing in the block diagram where the layers should end, and (c) shows
when the participant connects the marks forming the layers
Learning 3D Visualization Strategies 3055
Dow
nloa
ded
by [
Ort
a D
ogu
Tek
nik
Uni
vers
itesi
] at
01:
55 0
6 Fe
brua
ry 2
016
by drawing an extra figure that supported their analytic process. The strategy wasdeveloped after several attempts to find a perspective from which they could visualizethe cross-section shown in problem 9, the first problem that required integrating threefaces of the block diagram to visualize the cross-section. In both cases, participantsdrew a new figure using only the top face of the diagram as a reference (as the redcircle and arrow show in Figure 7(a)). Then they used this figure to imagine howthe layers of the top face would penetrate the block diagram when the slice was atan angle.Figure 7(b) shows the first pattern of layers drawn by one of these subjects, before
she began to implement her integration strategy. This was based on the visualization ofthe external patterns exposed on the top face of the block diagram. The ‘squares’ pic-tured in each corner of her diagram indicate the difficulty the participant had in envi-sioning how the internal layers of the structure would change with the angle of thecutting plane. But then, when she was explaining the steps followed to solve theproblem, she remembered the external figure she had drawn a few minutes beforewhen she was using the top face as a reference. Immediately, she decided to changethe ‘squares’ that she had drawn to be ‘triangles’, reflecting what she had learnedfrom her external figure. The red arrows illustrate this in Figure 8(b).
When participant 7 started the next exercise that also required integrating the threefaces of the block diagram to draw the cross-section (problem 9), she did not immedi-ately apply the strategy just learned. First she tried to solve the exercise employing thesame analytic techniques she had been using before the development of this new
Figure 7. It shows the sequence of actions in problem 7 that lead a subject to develop the strategy.The red arrow in (a) shows the drawing made to visualize the layers of the top face of the blockdiagram, whereas the red circle indicates the figure through which she could picture how thelayers would be seen when penetrating the block diagram. (b) Notes the application of this logicin her drawing slice, and how she changed the squares (layers without penetrating the figure), for
an angle
3056 D. Halpern et al.
Dow
nloa
ded
by [
Ort
a D
ogu
Tek
nik
Uni
vers
itesi
] at
01:
55 0
6 Fe
brua
ry 2
016
strategy, for example, marking points of reference to calculate where the layers shouldstart and end in the drawing slice. As can be seen in Figure 8(a), the subject first drewsquares in the block diagram between the layers and the angles, in order to know howwide each layer would be. Then she drew similar squares in the left side of her drawing,as bench marks, to visualize from which points the layers should be draw. This is indi-cated by the red arrows in Figure 8(a). However, after 10minutes, she encountered thesame difficulty in envisioning how the internal layers of the structure would change inrelation to the angle of the cutting plane.At this point, the subject focused again on the top face of the figure as she had in the
previous problem, but this time she tried to visualize how the internal layers of theblock diagram would be seen if they would be leveraged or raised to the top face. Inother words, she tried to see the top face of the block with the internal layers projectedon this face. However, since it was difficult for the participant to picture in her mindhow the internal layers would be seen projected on the top face of the diagram, shedrew an extra figure to visualize this projection. This is reflected in the red circle inFigure 9(a). Once the subject could visualize how the top face of the block would beseen with the projected layers, she repeated the procedure she had developed inproblem 7. She drew a new figure using the top face of the diagram and thenstarted to imagine the ‘top face’ layers penetrating into the figure. And then, after
Figure 8. The red arrow in (a) indicates how the subject visualized first the internal structure of theblock diagram without applying the strategy, whereas the red circle shows the drawing made by thesubject reflecting the top face of the block diagram. The red circle in (b) indicates the figure throughwhich she could picture how the layers would be seen when they penetrate the block diagram, and thearrow shows how she changed the squares (layers without penetrating the figure), for an angle
Learning 3D Visualization Strategies 3057
Dow
nloa
ded
by [
Ort
a D
ogu
Tek
nik
Uni
vers
itesi
] at
01:
55 0
6 Fe
brua
ry 2
016
she could picture the patterns of layers on the top face, she tried to visualize the internalstructure:
I started doing top-down, like sinking into the image, I started to imagine peeling this face,and then slowly go down into it, and then I realized that it’s going to be into it, and it’sgoing to be replaced by the other pattern.
Once she could picture how the layers would change with the angle, she drew a newfigure reflecting this new pattern, as can be seen in Figure 9(b), and with this approachshe correctly solved the problem and repaired the original slice she had drawn ‘Itwould be like a little triangle, and then slowly it’s going to be bigger, and bigger,and so another triangle came’. Interestingly, after this problem the subject definitelylearned this strategy and incorporated it in her pool of techniques, since she used itimmediately in the next two problems, skipping the analytic techniques employed pre-viously. In problems 7 and 9, it took 12 and 10 minutes, respectively, to solve the pro-blems, whereas in problems 10 and 11, when she implemented the strategyimmediately, it only took her 2 and 3 minutes, respectively.
4. Discussion
This paper focuses on identifying which viable strategies students use to infer andinterpret cross-sections of 3D objects. We have carried out the study with theintent of designing visualization software problems able to support the learning
Figure 9. An adapted Visualyzer/Analyzer model. In a subsequent act of visualization, V2,participants used the same ‘picture’ used in V1, but as a result of the analysis in A1, in which theycalculated the ‘bench marks’ to see where the layers would start, it has changed. That is, in V2compared these marks with the block diagram for accuracy, and A2 lead participants to theconstruction of a new picture to contrast how the layers would be affected by the angles. Andthen, based on these measurements, they went back to check the different faces of the blocks inorder to confirm the proportions (V3), by identifying what they believed would be the end of thelayers (A3), to finally connect the points marked previously. In any case, the result is an externalrepresentation in which the individual achieves some richer understanding of the original situation
3058 D. Halpern et al.
Dow
nloa
ded
by [
Ort
a D
ogu
Tek
nik
Uni
vers
itesi
] at
01:
55 0
6 Fe
brua
ry 2
016
processes exhibited by our participants. Our findings suggest that although spatialtransformation and perspective-taking techniques were immediately used by ourparticipants to visualize cross-section problems, both such processes were signifi-cantly augmented by analytic thinking. Subjects who employed analytic techniqueswere able to visualize more accurately the block diagram cutting planes than thosewho did not follow such strategies. Our research also showed that visualization ofcross-sections is an effortful process: participants could not mentally imagine theconfigurations of the layers when the angle of the cutting plane was not perpendicu-lar to such layers. They could only do so with external help (e.g. drawing an extrafigure) or through analytic strategies. Finally, our analysis also indicates that partici-pants employ general analytic strategies (trial and error) for extended periods andthen slowly adapt more focused strategies with practice until they arrive at a setof workable expert analytic strategies.
4.1. Theoretical Implications
Our findings have implications for two main theoretical approaches in the visualiza-tion and problem-solving literature: (1) the distributed cognition framework and (2)theoretical models that view visual and analytic reasoning as complements. Regard-ing the distributed cognition approach, the study indicates that only participantswho used an external element (a visual–spatial representation) to support theirinternal computation can mentally manipulate the structure of the block diagramsand the mapping of their layers on to the cross-section plane. These findings areconsistent with distributed cognition theories, which hold that people tend tooffload internal visualization processes onto the manipulation of external represen-tations: all the participants during the study decided at some point to off-load theircognitive efforts to perceptual-motor actions such as using an external visualization,or simply rotating the paper (instead of rotating the block diagrams mentally),showing a preference for less cognitive effort as the minimum memory model pre-dicts. Our results are also aligned with previous findings in the problem-solving lit-erature, which suggests that as individuals learn new strategies, individuals applyschemas and draw inferences from new information in problem-solving situations(Larkin et al., 1980).Regarding theoretical models that view visual and analytic reasoning as comp-
lements, our findings corroborated that visualization and analytic thinking can beconsidered two interacting modes that are complemented by each other inproblem-solving tasks. Specifically, our results support the V/A model, which con-siders visual and analytic reasoning as counterparts (Presmeg, 1992). Interestingly,the intertwined pattern proposed by the V/A model was seen in most of the subjectswho engaged in analytical strategies, specifically in those participants who usedthem to manipulate the patterns that appeared on the cross-section when thecutting plane was at an angle to the planes of reference. Figure 6 illustrates thisprocess, in which participants start to draw regular layers visualized in the blockdiagram (V1); then they calculate the ‘bench marks’ to see where the layers start
Learning 3D Visualization Strategies 3059
Dow
nloa
ded
by [
Ort
a D
ogu
Tek
nik
Uni
vers
itesi
] at
01:
55 0
6 Fe
brua
ry 2
016
(A1); consequently they compare these marks with the block diagram for accuracy(V2); to contrast how the layers would be affected by the angles (A2), and then,based on these measurements, they go back to check the different faces of theblocks in order to confirm the proportions (V3), in order to identify what theybelieve would be the end of the layers (A3), to finally connect the points markedpreviously. Figure 9 adapts the V/A model by describing the different stepsemployed by participants.Lastly, the analyses of the strategies developed by participants were also consistent
with findings in the use of strategic processing in academic performance. Researchhas shown that academic performance is highly related to students who monitor andregulate their cognitive processing appropriately during task performance (Chiet al., 1981). In our study, participants who reviewed the steps followed to solve theproblems were able to develop and improve their performance, as was illustrated bythe description of how participant 7 developed her strategy.
4.2. Practical Implications
Based on the cross-section visualization strategies employed by the participants, andsupported by previous experiences that have demonstrated how visualization softwarecan enhance 3D geometric proficiency by improving user’s abilities to build spatialimages (Hauptman, 2010), we suggest five main aspects to be considered in thedesign of the software aimed to facilitate learning effective internal processes invisual comprehension:First, we found that subjects physically or mentally rotated their block diagrams to
help in visualizing the cross-sections from their own perspective: participants preferredto arrange the 2D figure so that the X–Z plane was parallel to them instead turned at a45 degree angle from this position. We also saw that the same block diagrams—especially those with a horizontal cutting plane—were visualized differently by sub-jects: with participants mentioning trying to visualize the cross-section by looking atthe problem from the top of it (that is, in the X–Y plane); others attempted to visualizethe diagrams from the bottom (still the X–Y plane). Overall, participants who showedmore ability to change their perspective while solving the problems had consistentlyhigher performance. In fact, Table 1 shows that after problem 9, only subjects whoused one of these strategies could solve the remaining problems. From this analysiswe can deduce that it may be useful for users to control their perspective whenviewing 3D problems in order to more accurately visualize a cross-section. Conse-quently, the first solution for aiding the student in problem-solving suggests a compu-ter application capable of rotating 3D figures in which the users have the opportunityto rotate the block diagrams but not by stepwise rotations, but rather by the selection ofa viewing perspective.Second, the analysis showed that it was helpful for subjects to put the letters (ABCD)
as points of reference in drawing the cross-section, imitating the original positions ofthe cutting plane in the block diagram. By using the reference points, subjectswere able to better comprehend the arrangement of the figure and understand their
3060 D. Halpern et al.
Dow
nloa
ded
by [
Ort
a D
ogu
Tek
nik
Uni
vers
itesi
] at
01:
55 0
6 Fe
brua
ry 2
016
spatial relationship with the other elements in the block diagram. Also, by compar-ing their drawing with the original diagram, it was easier for them to move androtate the drawing to fit the block diagram orientation. Consequently, the software appli-cation should support the use of references (e.g. cardinal points) to orient and guideusers in determining the relative position of the spatially arranged items in the blockdiagram.
Third, our study indicated that participants often became confused trying to dis-tinguish which elements to include in their cross-section drawing because thedensity and complexity of irrelevant features in the block diagram interfered withtheir selection. This ‘information overload’ effect was observed to cause subjects toemploy strategies such as (1) blocking the non-useful areas in the diagram to helpthem in inferring the cross-section, and/or (2) drawing extensions to the cuttingplane in order to clearly define the area included in the cross-section. Based onthese responses, the software learning application should allow problem solvers tohighlight those areas included in the cutting plane (e.g. marking them with a differentcolor). It should also provide a design feature in which problem solvers can highlightdifferent features and areas of the block diagram giving users the possibility to observeseparately the different features that might be included in the cross-section. Thisdesign would also support the task decomposition strategy employed by manysubjects.Fourth, we found that participants who reviewed the steps followed were able to
develop and improve their performance. This is consistent with findings in educationresearch, which has demonstrated that students who relate their understanding toprinciples found in their texts and revisit their own understanding of problems learnand perform better. Thus, we recommend integrating a tracking function in thedesign of the software application that records the steps and approaches employedby users as they attempt to solve problems and gives users the capability to playbacktheir prior steps. We envision implementing this as an undo and redo function. Thedesign of this capability is also consistent with hypothesis-testing theories, whichsuggests that by providing problem solvers with feedback on their iterative process,they have more chances to learn viable solution strategies.Finally, our analysis shows that for all subjects, it was difficult to form a mental
image of a solution when the cutting plane was at an angle to the planes of reference.Only those participants who drew additional external figures and used analytical tech-niques were able to envision how the internal layers of a structure would change whenprojected at an angle on the cutting plane. The set of actions followed by subject 7 inour study suggest the following design for our 3D learning system. Subject 7 system-atically approached the design by looking at how patterns on the top face of the blockmight be projected on the cutting plane, then how patterns on each of the side facesmight be projected if the cutting plane were perpendicular, then changed by 10degrees from the perpendicular, then 20 degrees and so on. To copy this approach,our learning system will involve giving multiple problems that are ‘tweaked’ slightlyand presented in succession to the problem solver. The first problem would havea cutting plane that is perpendicular to the presentation planes. The follow-up
Learning 3D Visualization Strategies 3061
Dow
nloa
ded
by [
Ort
a D
ogu
Tek
nik
Uni
vers
itesi
] at
01:
55 0
6 Fe
brua
ry 2
016
problem would be the same but use a cutting plane that is set at 10 degrees from theperpendicular. The next problem would have a cutting plane set at 20 degrees and soon. This procedure would be employed with simple block diagrams and then proceedto more complex diagrams. Similarly, we will present problems in which the cuttingplane is parallel to the z-axis and perpendicular to the x–y plane of the problems butalso switch to cutting planes that are parallel the y-axis.Overall, the learning software we are proposing will track the success of users in
solving progressively more difficult 3D slice visualizations and adapt its problem pres-entation to progressively present those visualizations which the user is having the mostdifficulty with beginning with easier problems that slowly get more difficult and thus,suggest the analytic strategies to solve them.
5. Conclusion
The study investigated the range of strategies individuals develop to infer and interpretcross-sections of 3D objects with the goal of building training applications that inte-grate these strategies. Our results suggest that although spatial transformation and per-spective-taking techniques are useful for visualizing cross-section problems, thesevisual processes are augmented by analytical thinking which evolve through practiceinto a set of progressively more expert strategies. We believe the conclusions obtainedin the analysis may be useful to integrate into the design of intelligent software thatfacilitates internal processes such as visual learning and comprehension. Overall ourinvestigation yielded five major findings for this purpose. First, the software shouldallow users to control the perspective through which they view 3D information inorder to more accurately visualize the cross-section. Second, it should support theuse of reference points to orient users in determining the relative position of thespatially arranged items in the block diagram. Third, it should provide a designfeature in which the problem solver can highlight different features of the blockdiagram in order to enable users to observe individually the different features thatmight be included in a cross-section. Fourth, it should have a tracking function thatrecords the steps and approaches employed by users as they attempt to solve problemsand to allow users to playback the steps taken. And lastly, we believe that the softwareshould incorporate an analytical technique to aid the user in envisioning for examplehow the internal layers of a structure change when either the cutting plane or the fea-tures change orientation.
Disclosure Statement
No potential conflict of interest was reported by the authors.
Funding
This work was supported by the National Science Foundation under Grant #0753176.
3062 D. Halpern et al.
Dow
nloa
ded
by [
Ort
a D
ogu
Tek
nik
Uni
vers
itesi
] at
01:
55 0
6 Fe
brua
ry 2
016
References
Ainsworth, S. E. (2006). DeFT: A conceptual framework for learning with multiple representations.Learning and Instruction, 16, 183–198.
Black, A. A. (2005). Spatial ability and earth science conceptual understanding. Journal of GeoscienceEducation, 53(4), 402–414.
Buckley, B. C. (2000). Interactive multimedia and model-based learning in biology. InternationalJournal of Science Education, 22(9), 895–935.
Charmaz, K. (2006). Constructing grounded theory: A practical guide through qualitative research.London: Sage.
Chi, M., Feltovich, P., & Glaser, R. (1981). Categorization and representation of physics problemsby experts and novices. Cognitive Sciences, 5, 121–152.
Cohen, C. A., & Hegarty, M. (2007). Individual differences in use of external visualisations toperform an internal visualisation task. Applied Cognitive Psychology, 21(6), 701–711.
Cook, M. P. (2006). Visual representations in science education: The influence of prior knowledgeand cognitive load theory on instructional design principles. Science Education, 90, 1073–1091.
Ericsson, K. A., & Simon, H. A. (1998). How to study thinking in everyday life: Contrasting think-aloud protocols with descriptions and explanations of thinking.Mind, Culture, and Activity, 5(3),178–186.
Feng, J., Spence, I., & Pratt, J. (2007). Playing an action video game reduces gender differences inspatial cognition. Psychological Science, 18, 850–855.
French, J. W., Ekstrom, R. B., & Price, L. A. (1969).Manual for kit of reference tests for cognitive factors.Princeton, NJ: Educational Testing Service.
Furió, C., & Calatayud, M. L. (1996). Difficulties with the geometry and polarity of molecules.Journal of Chemical Education, 73, 36–41.
Gick, M. L. (1986). Problem-solving strategies. Educational Psychologist, 21(1–2), 99–120.Gilbert, J. K. (2007). Visualization: A metacognitive skill in science and science education. In J. K.
Gilbert, M. Reiner, & M. Nakhleh (Eds.), Visualization: Theory and practice in science education(pp. 9–27). Dordrecht: Springer.
Glaser, B. G. (1978). Theoretical sensitivity: Advances in the methodology of grounded theory. Mill Valley,CA: Sociology Press.
Hauptman, H. (2010). Enhancement of spatial thinking with Virtual Spaces 1.0. Computers &Education, 54(1), 123–135.
Hegarty, M. (1992). Mental animation: Inferring motion from static diagrams of mechanicalsystems. Journal of Experimental Psychology: Learning, Memory and Cognition, 18(5), 1084–1102.
Hegarty, M. (2010). Components of spatial intelligence. Psychology of Learning and Motivation, 52,265–297.
Heo, M., & Hirtle, S. (2001). An empirical comparison of visualization tools to assist retrieval on theWeb. Journal of the American Society for Information Science and Technology, 52(8), 666–675.
Kali, Y., & Orion, N. (1996). Spatial abilities of high-school students in the perception of geologicstructures. Journal of Research in Science Teaching, 33(4), 369–391.
Keehner, M., Hegarty, M., Cohen, C. A., Khooshabeh, P., & Montello, D. R. (2008). Spatialreasoning with external visualizations: What matters is what you see, not whether you interact.Cognitive Science, 32, 1099–1132.
Kozma, R., Chin, E., Russell, J., & Marx, N. (2000). The roles of representations and tools in thechemistry laboratory and their implications for chemistry learning. The Journal of the LearningSciences, 9(2), 105–143.
Larkin, J., McDermott, J., Simon, D., & Simon, H. (1980). Expert and novice performance insolving physics problems. Science, 208, 1335–1342.
Learning 3D Visualization Strategies 3063
Dow
nloa
ded
by [
Ort
a D
ogu
Tek
nik
Uni
vers
itesi
] at
01:
55 0
6 Fe
brua
ry 2
016
Linn, M. C., & Petersen, A. C. (1985). Emergence and characterization of sex differences in spatialability: A meta-analysis. Child Development, 56, 1479–1498.
Marshall, P. (2007). Do tangible interfaces enhance learning? In Proceedings of the 1st internationalconference on Tangible and embedded interaction, Baton Rouge, LA, USA (pp. 163–170). NewYork, NY: ACM.
Mayer, R. E., & Gallini, J. K. (1990). When is an illustration worth ten thousand words? Journal ofEducational Psychology, 82, 715–726.
Mayer, R. E., & Moreno, R. (1998). A cognitive theory of multimedia learning: Implications fordesign principles. Journal of Educational Psychology, 91(2), 358–368.
Newell, A., & Simon, H. A. (1972).Human problem solving (Vol. 104, No. 9). Englewood Cliffs, NJ:Prentice-Hall.
Piburn, M. D., Reynolds, S. J., McAuliffe, C., Leedy, D. E., Birk, J. P., & Johnson, J. K. (2005). Therole of visualization in learning from computer-based images. International Journal of ScienceEducation, 27(5), 513–527.
Presmeg, N. C. (1992). Prototypes, metaphors, metonymies and imaginative rationality in highschool mathematics. Educational Studies in Mathematics, 23, 595–610.
Pozzer-Ardenghi, L., & Roth, W. M. (2005). Making sense of photographs. Science Education, 89(2),219–241.
Rapp, D. N., & Kurby, C. A. (2008). The ‘ins’ and ‘outs’ of learning: Internal representations andexternal visualizations. In J. K. Gilbert, M. Reiner, & M. Nakhleh (Eds.), Visualization: Theoryand practice in science education (Vol. 3, pp. 29–52). Dordrecht: Springer.
Russell-Gebbett, J. (1985). Skills and strategies—Pupils’ approaches to three-dimensional problemsin biology. Journal of Biological Education, 19(4), 293–298.
Shneiderman, B. (1997). Direct manipulation for comprehensible, predictable and controllable userinterfaces. In Proceedings of the 2nd international conference on Intelligent user interfaces, Orlando, FL(pp. 33–39). New York, NY: ACM.
Siegler, R. S. (2006). Microgenetic analyses of learning. In W. Damon & R. M. Lerner (Series Eds.)& D. Kuhn & R. S. Siegler (Vol. Eds.),Handbook of child psychology: Volume 2: Cognition, percep-tion, and language (6th ed., pp. 464 – 510). Hoboken, NJ: Wiley.
Stieff, M., & Raje, S. (2008, June). Expertise & spatial reasoning in advanced scientific problemsolving. In Proceedings of the 8th international conference on International conference for the learningsciences—Volume 2 (pp. 366–373). Mahwah, NJ: Erlbaum.
Stylianou, D. A. (2002). On the interaction of visualization and analysis: The negotiation of a visualrepresentation in expert problem solving. The Journal of Mathematical Behavior, 21(3), 303–317.
Sweller, J. (1988). Cognitive load during problem solving: Effects on learning. Cognitive Science, 12(2), 257–285.
Sweller, J. (2004). Instructional design consequences of an analogy between evolution by naturalselection and human cognitive architecture. Instructional Science, 32, 9–31.
Terlecki, M. S., Newcombe, N. S., & Little, M. (2008). Durable and generalized effects of spatialexperience on mental rotation: Gender differences in growth patterns. Applied Cognitive Psychol-ogy, 22(7), 996–1013.
Treagust, D. F., Chittleborough, G. D., & Mamiala, T. L. (2003). The role of submicroscopicrepresentations in chemical explanations. International Journal of Science Education, 25, 1353–1368.
Tzuriel, D., & Egozi, G. (2010). Gender differences in spatial ability of young children: The effects oftraining and processing strategies. Child Development, 81(5), 1417–1430.
Uttal, D. H., & Doherty, K. O. (2008). Comprehending and learning from ‘visualizations’: A devel-opmental perspective. In J. K. Gilbert, M. Reiner, & M. Nakhleh (Eds.), Visualization: Theoryand practice in science education (pp. 53–72). Dordrecht: Springer Netherlands.
Webb, R.M., Lubinski, D., & Benbow, C. P. (2007). Spatial ability: A neglected dimension in talentsearches for intellectually precocious youth. Journal of Educational Psychology, 99, 397–420.
3064 D. Halpern et al.
Dow
nloa
ded
by [
Ort
a D
ogu
Tek
nik
Uni
vers
itesi
] at
01:
55 0
6 Fe
brua
ry 2
016
Winn, W., & Jackson, R. (1999). Fourteen propositions about educational uses of virtual reality.Educational Technology, 39(4), 5–14.
Wraga, M., Creem, S. H., & Profitt, D. R. (2000). Updating displays after imagined object andviewer rotations. Journal of Experimental Psychology: Learning, Memory, and Cognition, 26,151–168.
Wright, R., Thompson, W. L., Ganis, G., Newcombe, N. S., & Kosslyn, S. M. (2008). Traininggeneralized spatial skills. Psychonomic Bulletin & Review, 15, 763–771.
Wu, H. K., & Shah, P. (2004). Exploring visuospatial thinking in chemistry learning. Science Edu-cation, 88(3), 465–492.
Zazkis, R., Dubinsky, E., & Dautermann, J. (1996). Coordinating visual and analytic strategies: Astudy of students’ understanding. Journal for Research in Mathematics Education, 27(4), 435–437.
Learning 3D Visualization Strategies 3065
Dow
nloa
ded
by [
Ort
a D
ogu
Tek
nik
Uni
vers
itesi
] at
01:
55 0
6 Fe
brua
ry 2
016